Abstract
Abstract The arranged paths of dominoes have many shapes. The scaling law for the propagation speed of domino toppling has been extensively investigated. However, in all previous investigations the scaling law for the velocity of domino toppling motion in curved lines was not taken into account. In this study, the finite-element analysis (FEA) program ABAQUS was used to discuss the scaling law for the propagation speed of domino toppling motion in curved lines. It is shown that the domino propagation speed has a rising trend with increasing domino spacing in a straight line. It is also found that domino propagation speed is linearly proportional to the square root of domino separation. This research proved that the scaling law for the speed of domino toppling motion given by Sun [Scaling law for the propagation speed of domino toppling. AIP Adv. 2020;10(9):095124] is true. Moreover, the shape of domino arrangement paths has no influence on the scaling law for the propagation speed of dominoes, but can affect the coefficient of the scaling law for the velocity. Therefore, the amendatory function for the propagation speed of dominoes in curved lines was formulated by the FEA data. On one hand, the fitted amendatory function, φ revise {\varphi }_{{\rm{revise}}} , provides the simple method for a domino player to quickly estimate the propagation speed of dominoes in curved lines; on the other hand, it is the rationale for the study of the domino effect.
Highlights
The arranged paths of dominoes have many shapes
To study the law between the propagation speed of dominoes and domino spacing in the straight paths accurately, ABAQUS was used to simulate the numerical analysis for the propagation speed of 17 domino models with various domino separations
The law for domino propagation velocity and spacing satisfies the scaling law for the propagation speed of dominoes given in the literature [15]
Summary
Abstract: The arranged paths of dominoes have many shapes. The scaling law for the propagation speed of domino toppling has been extensively investigated. Program ABAQUS was used to discuss the scaling law for the propagation speed of domino toppling motion in curved lines. The functional relation is Keywords: domino, toppling motion, scaling law, velocity, curved paths. Scaling law for velocity of domino toppling motion in curved paths relationship between velocity and domino width, height, and spacing was derived. To obtain a simple explicit scaling law for the propagation speed of dominoes, the function f δ α λ ( ) ≈ C( ) was δ λ deduced by curve fitting of the experimental data. In the present work, the finite-element analysis (FEA) program AQABUS was used to explore the mechanics of domino toppling motion in curved paths. The scaling law for the propagation speed of domino toppling in different curved paths was proposed by data fitting. When the curvature is zero, the scaling law obtained in the present work is consistent with the scaling law proposed by Sun [15]
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